1. When divided by x - 1, the polynomial P(x) = x5 + 2x3 + Ax + B, where A and B are constants, the remainder is equal to 2. When P(x) is divided by x + 3, the remainder is equal -314. Find A and B.
2. Find all points of intersections of the 2 circles defined by the equations
(x - 2)2 + (y - 2)2 = 4
(x - 1)2 + (y - 1)2 = 4
3. If 200 is added to a positive integer I, the result is a square number. If 276 is added to to the same integer I, another square number is obtained. Find I.
4. The sum of the first three terms of a geometric sequence is equal to 42. The sum of the squares of the same terms is equal to 1092. Find the three terms of the sequence.
5. A rock is dropped into a water well and it travels approximately 16t2 in t seconds. If the splash is heard 3.5 seconds later and the speed of sound is 1087 feeVsecond, what is the height of the well?
6. Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately tum around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?
7. Find the constants a and b so that all the 4 lines whose equation are given by
x+y=-1
-x + 3y = -11
ax + by = 4
2ax - by = 2
pass through the same point.